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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Thursday, July 20, 2000}
\centerline{Sequoia Hall Rm. 200}

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\centerline{\sl Efstathia Bura}
\centerline{\sl Assistant Professor}
\centerline{\sl Department of Statistics}
\centerline{\sl The George Washington University}
\centerline{\sl Washington, DC}
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\centerline{\bf Assessing the structural dimension of regressions}
\centerline{\bf using parametric and nonparametric inverse regression}
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The structural dimension of a regression is defined to be the dimension of
the linear subspace spanned by projections of the $p$-dimensional regressor
vector $X$, which contains part or all of the modelling information for
the regression of a random variable $Y$ on $X$. New assessment methods
for the dimension of a regression, at the outset of the analysis, are
proposed. Parametric and nonparametric inverse regression are used to
estimate the structural dimension, and a lower bound on the structural
dimension, respectively. Smooth parametric and nonparametric curves are
fitted to the $p$ inverse regressions. No restrictions are placed on the
distribution of the regressor vector except for the {\bf linearity
condition}. Asymptotic chi-square tests for dimension are obtained in both
cases. A simulation study is also presented.

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